Contribution to Isotope Shifts by the Charge Distribution within a Neutron: A Naive, First-Order Perturbation Approach

1969 ◽  
Vol 37 (5) ◽  
pp. 479-481
Author(s):  
Robert Ter Bush
Keyword(s):  
Charge Distribution ◽  
Order Perturbation ◽  
Perturbation Approach ◽  
Isotope Shifts ◽  
First Order ◽  
First Order Perturbation

Nonlinear self-phase-modulation effects: a vectorial first-order perturbation approach

1995 ◽  
Vol 20 (5) ◽  
pp. 456 ◽  
Author(s):  
Velko P. Tzolov ◽  
Nicolas Godbout ◽  
Suzanne Lacroix ◽  
Marie Fontaine
Keyword(s):  
Phase Modulation ◽  
Order Perturbation ◽  
Perturbation Approach ◽  
Self Phase Modulation ◽  
First Order ◽  
First Order Perturbation

Stochastic Homogenized Properties for Honeycomb Microstructure Based on First Order Perturbation

2014 ◽  
Vol 695 ◽  
pp. 516-520
Author(s):  
Khairul Salleh Basaruddin
Keyword(s):  
Homogenization Method ◽  
Order Perturbation ◽  
Perturbation Approach ◽  
Scale Problem ◽  
Microstructure Design ◽  
First Order ◽  
Multi Scale ◽  
Macroscopic Property ◽  
Gaussian Normal Distribution ◽  
First Order Perturbation

A stochastic analysis of multi-scale problem in honeycomb microstructure was introduced in this paper to determine the variation of macroscopic homogenized properties considering uncertainty of micro-property. By assuming the fluctuation of micro-property, specifically the Young's modulus, is in Gaussian normal distribution, the macroscopic (homogenized) properties was formulated in stochastic manner based on first order perturbation approach. Next, the macroscopic property of honeycomb microstructure considering the geometrical defect that might be occurred in manufacturing process was also predicted. The numerical results showed that even with minor geometrical defect could affect the macroscopic properties. It proved the essential of stochastic homogenization method in predicting the reliable macroscopic property for microstructure design.

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